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Table 1.
Notations used in this work.
| Quantity | Description |
|---|---|
| ψg | Set of parameters describing a foreground galaxy. |
| ψs | Set of parameters describing a background source. |
| Pg(ψg) | Probability distribution of the foreground galaxy population. |
| Ps(ψs) | Probability distribution of the background source population. |
| S | Selection criteria of the strong lens survey. |
| PSL(ψg, ψs|S) | Probability distribution of the strong lens population given the survey selection criteria. |
| β | Angular position of the source. |
 |
Set of background source parameters, excluding the angular position. |
 |
Strong lensing cross-section of a galaxy with parameters ψg, relative to a source with parameters  . |
| d | Array of observational data (of the entire survey, or relative to a generic system). |
| Ω | Volume of the data space defined by the selection criteria of the survey. |
| η | Set of parameters describing the population of foreground galaxies. |
| Ns | Number of strongly lensed sources associated to a foreground galaxy. |
| λ | Expectation value of the number of strongly lensed sources associated to a galaxy. |
| nbkg | Projected number density of background sources. |
| P(ψs|Lens, S) | Probability distribution of the source parameters, given that the source is strongly lensed. |
| θ | Angular coordinate in the image plane of a strong lens. |
| α(θ) | Deflection angle of the lens. |
| θEin | Einstein radius of a lens, in angular units. |
| γ | Slope of the density profile of a power-law lens. |
| θ1, θ2 | Coordinates of image 1 and 2 (the main image of a strongly lensed source and the counter image). |
| 𝒩(μ, σ2) | Normal distribution with mean μ and variance σ2. |
| ms | Source intrinsic (unlensed) magnitude. |
 |
Knee of the source magnitude distribution function. |
| αs | Faint-end slope of the source magnitude distribution function. |
| μ(θ) | Lensing magnification at image position θ. |
| m1, m2 | True magnitudes of images 1 and 2. |
 |
Observed magnitudes of images 1 and 2. |
| ϵm | Observational uncertainty (1σ) on the image magnitudes. |
| mmax | Maximum allowed magnitude of image 2, for a system to be defined a strong lens. |
| μEin | Parameter describing the mean log θEin of the galaxy population. |
| σEin | Parameter describing the scatter in log θEin of the galaxy population. |
| μγ | Parameter describing the mean γ of the galaxy population. |
| σγ | Parameter describing the scatter in γ of the galaxy population. |
| ξasymm | Image configuration asymmetry, defined in Eq. (30). |
 |
Value of θEin needed to reproduce the observed image positions, for a given γ. |
| β* | Value of β needed to reproduce the observed image positions, for a given γ. |
| detJ | Jacobian determinant of the variable change (log θEin, γ)→(θ1, θ2). |
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